An investigation was conducted in a hypersonic shock tunnel to study the laminar boundary-layer transition on a highly cooled 10° cone of 4 ft. length over the Mach-number range of 8·5 to 10·5 with a stagnation temperature of 1400 °K. The effects on transition of tip surface roughness, tip bluntness, and ± 2° angle of attack were investigated. With fast-response, thin film surface heat-transfer gauges, it was possible to detect the passage of turbulent bursts which appeared at the beginning of transition. Pitot-tube surveys and schlieren photographs of the boundary layer were obtained to verify the interpretation of the heat-transfer data. It was found that the surface roughness greatly promoted transition in the proper Reynolds-number range. The Reynolds numbers for the beginning and end of transition at the 8·5 Mach-number location were 3·8 × 106−9·6 × 106 and 2·2 × 106−4·2 × 106 for the smooth sharp tip and rough sharp tip respectively. The local skin-friction data, determined from the Pitot-tube survey, agreed with the heat-transfer data obtained through the modified Reynolds analogy. The tip-bluntness data showed a strong delay in the beginning of transition for a cone base-to-tip diameter ratio of 20, approximately a 35% increase in Reynolds number over that of the smooth sharp-tip case. The angle-of-attack data indicated the cross flow to have a strong influence on transition by promoting it on the sheltered side of the cone and delaying it on the windward side.

Two-dimensional flow of a second-order fluid near a stagnation point occurring on a flat plate which is performing harmonic oscillations in its own plane is considered. The equations have been integrated by the Kármán-Pohlhausen method for small values of ω, the frequency of the oscillation of the plate, and the W.B.K. method is applied to solve the equations for high values of ω. The velocity profile within the boundary-layer region and the shearing stress on the plate have been obtained in both the cases. The oscillation of the shearing stress has a phase lead over the oscillation of the plate. This phase lead decreases with increase of the second-order effect for small values of ω.

The interaction was observed between a supersonic free jet of partially ionized argon and the magnetic field of a coil concentric with the jet. Nominal values of the parameters were: Mach number, 3; Reynolds number, 1000; magnetic Reynolds number, 0·2; magnetic interaction parameter, 1; Hall parameter, 1. The jet was strongly channelled. Axial and radial electric fields were observed in the jet with a net rise in potential across the interaction.

These observations were consistent with predictions based on the single fluid, macroscopic equations, and a simple slug flow model. The current equation was solved to second order in the Hall parameter giving a closed form expression for the Hall potential which agreed with the experiments for weak fields. Flow perturbations were calculated for Mach numbers of 3.11, 6.08, and 10.05, neglecting Hall currents; the calculations are in qualitative agreement with the experiments and show Joule heating to be the main factor in perturbing the flow at high Mach numbers.

Non-equilibrium inviscid flows behind a spherical-segment shock wave are investigated with the method of series truncation. This semi-analytical technique developed at Stanford is based on a systematic co-ordinate-perturbation scheme. The flow variables are expanded in series in powers of the longitudinal curvilinear co-ordinate leading away from the stagnation point. The problem is thus reduced to one of numerical integration of ordinary differential equations for functions of the normal co-ordinate. Unlike the similar situation of the Blasius series in boundary-layer theory, the present scheme–having to deal with elliptic equations–must resort to series truncation. As a consequence, a truncation error is introduced. The present paper shows a simple way of reducing this error.

The simplified air chemistry adopted is based on non-equilibrium dissociation and recombination of oxygen diluted in inert nitrogen. A wide spectrum of non-equilibrium régimes is investigated for a fixed set of flight conditions. In particular, near-frozen flows are followed to the vicinity of the stagnation point through a region of large temperature and concentration gradients located near the body. This equilibrium-drive region, arising from the singular nature of the frozen limit, is studied in some detail.

The large-eddy energy equilibrium hypothesis states that the largest eddies of a turbulent shear flow are in approximate energy equilibrium throughout a significant part of their lives. This hypothesis leads to a relationship between the mean rate of shear strain and the Reynolds shear stress which involves the scale of the large eddies. By assuming that the large-eddy scale is proportional to the standard deviation of the free turbulent boundary, or laminar superlayer, the validity of this hypothesis may be checked experimentally. Intermittency and mean velocity measurements made in five different two-dimensional shear flows are presented and these results, together with values calculated from Townsend's measurements in a two-dimensional wake, support the form of relationship suggested by the energy equilibrium hypothesis.

An analysis of the exact equations of the inviscid flow of a perfect gas over cusped concave bodies is described. The field is examined in the limit of infinite free-stream Mach number M∞. The slope of the shock wave in a small region adjacent to the leading edge is strongly dependent on M∞, while much further downstream the shock-wave slope is controlled primarily by the body slope. Consequently the region near the leading edge introduces into the field downstream a thin layer of gas, adjacent to the body, where the entropy is much lower than that of the gas above it. This layer is so dense that the gas velocity along it is not appreciably slowed by the pressure gradient along the body. However, it is so thin that there is little pressure change across it.

The well-known self-similar solutions to the hypersonic small-disturbance equations have previously only been used to study the flow on blunted slender convex surfaces. They are known to behave singularly at the body. It is shown that there is a region on concave power-law shapes where the self-similar solutions are the correct first approximation to the exact inviscid equations in the limit M∞ → ∞; and that, further, they predict the correct first-order surface pressure.

Numerical results for surface pressure from the similar solutions are presented, and comparisons are made with certain approximate theories available for more general shapes. Pressure measurements taken on a cubic surface in the Imperial College gun tunnel are presented and compared with the theoretical distributions.

The viscous structure of a separated eddy is investigated for two cases of simplified geometry. In § 1, an analytical solution, based on a linearized model, is obtained for an eddy bounded by a circular streamline. This solution reveals the flow development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number, in the manner envisaged by Batchelor. Quantitatively, the solution shows that a significant inviscid core exists for a Reynolds number greater than 100. At low Reynolds number the vortex centre shifts in the direction of the boundary velocity until the inviscid core develops; at large Reynolds number, the inviscid vortex core is symmetric about the centre of the circle, except for the effect of the boundary-layer displacement-thickness. Special results are obtained for velocity profiles, skin-friction distribution, and total power dissipation in the eddy. In addition, results of the method of inner and outer expansions are compared with the complete solution, indicating that expansions of this type give valid results for separated eddies at Reynolds numbers greater than about 25 to 50. The validity of the linear analysis as a description of separated eddies is confirmed to a surprising degree by numerical solutions of the full Navier–Stokes equations for an eddy in a square cavity driven by a moving boundary at the top. These solutions were carried out by a relaxation procedure on a high-speed digital computer, and are described in § 2. Results are presented for Reynolds numbers from 0 to 400 in the form of contour plots of stream function, vorticity, and total pressure. At the higher values of Reynolds number, an inviscid core develops, but secondary eddies are present in the bottom corners of the square at all Reynolds numbers. Solutions of the energy equation were obtained also, and isotherms and wall heat-flux distributions are presented graphically.

Large spanwise variations of boundary-layer thickness and surface shear have been found recently in wind tunnels designed to maintain two-dimensional flow. Bradshaw (1965) argues that these variations are caused by minute deflexions in the free-stream flow rather than by any intrinsic instability of the boundary layers. This paper is a study of the effect of a small, periodic transverse flow on a flat-plate boundary layer. The perturbation flow Reynolds number is assumed to be O(1) as it is in the experiments.

The correspondence between the eigenvalues for the problem of the onset of convection in a fluid confined between two horizontal plates and for the stability of viscous flow between two cylinders rotating at almost the same angular velocity has been known for some time. The recent work of Chandrasekhar (1961) has prompted the extension of the analogy to a larger group of rotating cylinder problems and their associated convection cases in which the primary temperature distribution is parabolic. This paper shows the analogy between these two problems and presents data which give the corresponding temperature distribution for a given ratio of angular velocities between the two cylinders. The equivalent Rayleigh numbers are listed for the Taylor numbers given by Chandrasekhar (1954). The eigenfunctions for several of the parabolic temperature profiles are determined. These results show that the single vortex convection pattern becomes a double vortex for certain initial temperature distributions. The critical Rayleigh numbers for the stability of a layer of water which is near 4 °C is also found by analogy.

An exothermal hydromagnetic discontinuity in a perfectly conducting gas is studied for the case of an arbitrarily orientated magnetic field. The evolutionary modes and the manner of variation of the physical properties for such phenomena are determined. The Hugoniot adiabatic is obtained and analysed.

A set of Jeffery–Hamel profiles (for radial, viscous, incompressible flow) have been shown by Fraenkel (1962, 1963) to approximate to profiles in certain two-dimensional divergent channels. The stability of a family of these profiles is investigated by a numerical solution of the Orr-Sommerfeld problem. Neutralstability curves are calculated in the (R,k)-planes (where R is the Reynolds number of the basic flow and k is the wave-number of the disturbance), and fairly low critical Reynolds numbers are found. For those profiles that have regions of reversed flow, negative wave velocities are found on the lower branch of the neutral curve, and also it is found that Rk tends to a finite limit as R → ∞ on the lower branch. These unexpected results are further discussed and verified by independent methods. The relation of the calculations to some experiments of Patterson (1934, 1935) is discussed.